Formula Chart for Numbers and Operations on the SBAC Test
Most people say that Math is hard for them. Does this sound like you? Are you wondering how to ace the SBAC Test? Well,
Math is like music: a set of rules that, when applied correctly, create beauty.
Do you want to succeed on the SBAC Test? You’ll need to know the rules. In the following chart, you’ll find the essential rules you’ll need to apply when solving Numbers and Operations Questions on the SBAC Test. Use the rules and create your own “math music.”
Also, be sure and utilize our four other formula charts as you prepare for this test:
Numbers and Operations Formulas for the SBAC
Category  Formula  Symbols  Comment 

Properties of Rational Numbers 
\(a+b=b+a\) \(a \cdot b = b \cdot a\) 
a, b = any constant or variable  Commutative Property 
Properties of Rational Numbers 
\(a+(b+c)=(a+b)+c\) \(a \cdot (b \cdot c)=(a \cdot b) \cdot c\) 
a, b, c = any constant or variable  Associative Property 
Properties of Rational Numbers 
\(a \cdot (b+c)=a \cdot b + a \cdot c\)  a, b, c = any constant or variable  Distributive Property 
Properties of Rational Numbers 
\(a+0=a\)  a = any constant or variable  Identity Property of Addition 
Properties of Rational Numbers 
\(a \cdot 1 = a\)  a = any constant or variable  Identity Property of Multiplication 
Properties of Rational Numbers 
\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}\)  a, b, c, d = any real number  Remember to simplify the fraction if possible. 
Properties of Rational Numbers 
\(\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c)}{(b \cdot d)}\)  a, b, c, d = any real number  Remember to simplify the fraction if possible. 
Properties of Rational Numbers 
\(\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{a \cdot d)}{(b \cdot c)}\)  a, b, c, d = any real number  Remember to simplify the fraction if possible. 
Properties of Rational Numbers 
\(a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}\)  a, b, c = any real number  Remember to simplify the fraction if possible. 
Properties of Exponents 
\(x^a \cdot x^b = x^{a+b}\) 
a, b, x = any real number 
Remember to simplify the fraction if possible. 
Properties of Exponents 
\(\frac{x^a}{x^b}=x^{ab}\) 
a, b, x = any real number 

Properties of Exponents 
\((x^a)^b = x^{a \cdot b}\) 
a, b, x = any real number 

Properties of Exponents 
\((x \cdot y)^a = x^a \cdot y^a\) 
a, x, y = any real number 

Properties of Exponents 
\(x^1 = x\) 
x = any real number 

Properties of Exponents 
\(P=(2 \cdot l)+(2 \cdot w)\)  x = any real number 

Properties of Exponents 
\(x^{a} = \frac {1}{x^a}\) 
a, x = any real number 

Percentages  \(a \cdot b\%=a \cdot \dfrac{b}{100}\) 
a = any real number b% = any percent 
Remember to simplify if possible. 
Percentages  \(\% = \dfrac{\vert ba \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100\) 
% = % increase or decrease a = new value b = original value c = amount of change 

Units  \(Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF\) 
Du = Desired Unit Su = Starting Unit CF = Conversion Factor 
Multiple steps may be needed 
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